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# In how many ways can the letters of the word GOSSAMERE be re

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In how many ways can the letters of the word GOSSAMERE be re [#permalink]  13 May 2019, 10:46
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In how many ways can the letters of the word GOSSAMERE be rearranged such that all S’s and M’s appear in the middle?

(A) $$\frac{9!}{2!*2!}$$

(B) $$\frac{7P_6}{2!*2!}$$

(C) $$\frac{7P_6}{2!} * \frac{3P_3}{2!}$$

(D) $$\frac{6P_6}{2!} * \frac{3P_3}{2!}$$

(E) $$\frac{10P_6}{2!} * \frac{3P_3}{2!}$$
[Reveal] Spoiler: OA

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Re: In how many ways can the letters of the word GOSSAMERE be re [#permalink]  14 May 2019, 08:35
When encountering GRE problems using C or P notation in the choices, consider logical elimination rather than working through the entire problem to save time and avoid unnecessary steps. In this case, we know that there will be three letters (two Ss and one M) used in a subset in the center of the arrangement and then six other letters to be arranged on the outside of those interior two Ss and M. So, look for a choice involving both choosing from both 6 and 3 terms. Only choice D properly articulates this situation and is the correct answer.
Re: In how many ways can the letters of the word GOSSAMERE be re   [#permalink] 14 May 2019, 08:35
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